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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.optim.nonlinear.scalar.gradient;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.analysis.solvers.BrentSolver;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.analysis.solvers.UnivariateSolver;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.MathInternalError;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.MathIllegalStateException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.TooManyEvaluationsException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.optim.OptimizationData;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.optim.PointValuePair;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.optim.ConvergenceChecker;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.optim.nonlinear.scalar.GradientMultivariateOptimizer;<a name="line.31"></a>
<FONT color="green">032</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.32"></a>
<FONT color="green">033</FONT>    <a name="line.33"></a>
<FONT color="green">034</FONT>    /**<a name="line.34"></a>
<FONT color="green">035</FONT>     * Non-linear conjugate gradient optimizer.<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;p&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     * This class supports both the Fletcher-Reeves and the Polak-Ribière<a name="line.37"></a>
<FONT color="green">038</FONT>     * update formulas for the conjugate search directions.<a name="line.38"></a>
<FONT color="green">039</FONT>     * It also supports optional preconditioning.<a name="line.39"></a>
<FONT color="green">040</FONT>     * &lt;/p&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>     *<a name="line.41"></a>
<FONT color="green">042</FONT>     * @version $Id: NonLinearConjugateGradientOptimizer.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.42"></a>
<FONT color="green">043</FONT>     * @since 2.0<a name="line.43"></a>
<FONT color="green">044</FONT>     */<a name="line.44"></a>
<FONT color="green">045</FONT>    public class NonLinearConjugateGradientOptimizer<a name="line.45"></a>
<FONT color="green">046</FONT>        extends GradientMultivariateOptimizer {<a name="line.46"></a>
<FONT color="green">047</FONT>        /** Update formula for the beta parameter. */<a name="line.47"></a>
<FONT color="green">048</FONT>        private final Formula updateFormula;<a name="line.48"></a>
<FONT color="green">049</FONT>        /** Preconditioner (may be null). */<a name="line.49"></a>
<FONT color="green">050</FONT>        private final Preconditioner preconditioner;<a name="line.50"></a>
<FONT color="green">051</FONT>        /** solver to use in the line search (may be null). */<a name="line.51"></a>
<FONT color="green">052</FONT>        private final UnivariateSolver solver;<a name="line.52"></a>
<FONT color="green">053</FONT>        /** Initial step used to bracket the optimum in line search. */<a name="line.53"></a>
<FONT color="green">054</FONT>        private double initialStep = 1;<a name="line.54"></a>
<FONT color="green">055</FONT>    <a name="line.55"></a>
<FONT color="green">056</FONT>        /**<a name="line.56"></a>
<FONT color="green">057</FONT>         * Constructor with default {@link BrentSolver line search solver} and<a name="line.57"></a>
<FONT color="green">058</FONT>         * {@link IdentityPreconditioner preconditioner}.<a name="line.58"></a>
<FONT color="green">059</FONT>         *<a name="line.59"></a>
<FONT color="green">060</FONT>         * @param updateFormula formula to use for updating the &amp;beta; parameter,<a name="line.60"></a>
<FONT color="green">061</FONT>         * must be one of {@link Formula#FLETCHER_REEVES} or<a name="line.61"></a>
<FONT color="green">062</FONT>         * {@link Formula#POLAK_RIBIERE}.<a name="line.62"></a>
<FONT color="green">063</FONT>         * @param checker Convergence checker.<a name="line.63"></a>
<FONT color="green">064</FONT>         */<a name="line.64"></a>
<FONT color="green">065</FONT>        public NonLinearConjugateGradientOptimizer(final Formula updateFormula,<a name="line.65"></a>
<FONT color="green">066</FONT>                                                   ConvergenceChecker&lt;PointValuePair&gt; checker) {<a name="line.66"></a>
<FONT color="green">067</FONT>            this(updateFormula,<a name="line.67"></a>
<FONT color="green">068</FONT>                 checker,<a name="line.68"></a>
<FONT color="green">069</FONT>                 new BrentSolver(),<a name="line.69"></a>
<FONT color="green">070</FONT>                 new IdentityPreconditioner());<a name="line.70"></a>
<FONT color="green">071</FONT>        }<a name="line.71"></a>
<FONT color="green">072</FONT>    <a name="line.72"></a>
<FONT color="green">073</FONT>        /**<a name="line.73"></a>
<FONT color="green">074</FONT>         * Available choices of update formulas for the updating the parameter<a name="line.74"></a>
<FONT color="green">075</FONT>         * that is used to compute the successive conjugate search directions.<a name="line.75"></a>
<FONT color="green">076</FONT>         * For non-linear conjugate gradients, there are<a name="line.76"></a>
<FONT color="green">077</FONT>         * two formulas:<a name="line.77"></a>
<FONT color="green">078</FONT>         * &lt;ul&gt;<a name="line.78"></a>
<FONT color="green">079</FONT>         *   &lt;li&gt;Fletcher-Reeves formula&lt;/li&gt;<a name="line.79"></a>
<FONT color="green">080</FONT>         *   &lt;li&gt;Polak-Ribière formula&lt;/li&gt;<a name="line.80"></a>
<FONT color="green">081</FONT>         * &lt;/ul&gt;<a name="line.81"></a>
<FONT color="green">082</FONT>         *<a name="line.82"></a>
<FONT color="green">083</FONT>         * On the one hand, the Fletcher-Reeves formula is guaranteed to converge<a name="line.83"></a>
<FONT color="green">084</FONT>         * if the start point is close enough of the optimum whether the<a name="line.84"></a>
<FONT color="green">085</FONT>         * Polak-Ribière formula may not converge in rare cases. On the<a name="line.85"></a>
<FONT color="green">086</FONT>         * other hand, the Polak-Ribière formula is often faster when it<a name="line.86"></a>
<FONT color="green">087</FONT>         * does converge. Polak-Ribière is often used.<a name="line.87"></a>
<FONT color="green">088</FONT>         *<a name="line.88"></a>
<FONT color="green">089</FONT>         * @since 2.0<a name="line.89"></a>
<FONT color="green">090</FONT>         */<a name="line.90"></a>
<FONT color="green">091</FONT>        public static enum Formula {<a name="line.91"></a>
<FONT color="green">092</FONT>            /** Fletcher-Reeves formula. */<a name="line.92"></a>
<FONT color="green">093</FONT>            FLETCHER_REEVES,<a name="line.93"></a>
<FONT color="green">094</FONT>            /** Polak-Ribière formula. */<a name="line.94"></a>
<FONT color="green">095</FONT>            POLAK_RIBIERE<a name="line.95"></a>
<FONT color="green">096</FONT>        }<a name="line.96"></a>
<FONT color="green">097</FONT>    <a name="line.97"></a>
<FONT color="green">098</FONT>        /**<a name="line.98"></a>
<FONT color="green">099</FONT>         * The initial step is a factor with respect to the search direction<a name="line.99"></a>
<FONT color="green">100</FONT>         * (which itself is roughly related to the gradient of the function).<a name="line.100"></a>
<FONT color="green">101</FONT>         * &lt;br/&gt;<a name="line.101"></a>
<FONT color="green">102</FONT>         * It is used to find an interval that brackets the optimum in line<a name="line.102"></a>
<FONT color="green">103</FONT>         * search.<a name="line.103"></a>
<FONT color="green">104</FONT>         *<a name="line.104"></a>
<FONT color="green">105</FONT>         * @since 3.1<a name="line.105"></a>
<FONT color="green">106</FONT>         */<a name="line.106"></a>
<FONT color="green">107</FONT>        public static class BracketingStep implements OptimizationData {<a name="line.107"></a>
<FONT color="green">108</FONT>            /** Initial step. */<a name="line.108"></a>
<FONT color="green">109</FONT>            private final double initialStep;<a name="line.109"></a>
<FONT color="green">110</FONT>    <a name="line.110"></a>
<FONT color="green">111</FONT>            /**<a name="line.111"></a>
<FONT color="green">112</FONT>             * @param step Initial step for the bracket search.<a name="line.112"></a>
<FONT color="green">113</FONT>             */<a name="line.113"></a>
<FONT color="green">114</FONT>            public BracketingStep(double step) {<a name="line.114"></a>
<FONT color="green">115</FONT>                initialStep = step;<a name="line.115"></a>
<FONT color="green">116</FONT>            }<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>            /**<a name="line.118"></a>
<FONT color="green">119</FONT>             * Gets the initial step.<a name="line.119"></a>
<FONT color="green">120</FONT>             *<a name="line.120"></a>
<FONT color="green">121</FONT>             * @return the initial step.<a name="line.121"></a>
<FONT color="green">122</FONT>             */<a name="line.122"></a>
<FONT color="green">123</FONT>            public double getBracketingStep() {<a name="line.123"></a>
<FONT color="green">124</FONT>                return initialStep;<a name="line.124"></a>
<FONT color="green">125</FONT>            }<a name="line.125"></a>
<FONT color="green">126</FONT>        }<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>        /**<a name="line.128"></a>
<FONT color="green">129</FONT>         * Constructor with default {@link IdentityPreconditioner preconditioner}.<a name="line.129"></a>
<FONT color="green">130</FONT>         *<a name="line.130"></a>
<FONT color="green">131</FONT>         * @param updateFormula formula to use for updating the &amp;beta; parameter,<a name="line.131"></a>
<FONT color="green">132</FONT>         * must be one of {@link Formula#FLETCHER_REEVES} or<a name="line.132"></a>
<FONT color="green">133</FONT>         * {@link Formula#POLAK_RIBIERE}.<a name="line.133"></a>
<FONT color="green">134</FONT>         * @param checker Convergence checker.<a name="line.134"></a>
<FONT color="green">135</FONT>         * @param lineSearchSolver Solver to use during line search.<a name="line.135"></a>
<FONT color="green">136</FONT>         */<a name="line.136"></a>
<FONT color="green">137</FONT>        public NonLinearConjugateGradientOptimizer(final Formula updateFormula,<a name="line.137"></a>
<FONT color="green">138</FONT>                                                   ConvergenceChecker&lt;PointValuePair&gt; checker,<a name="line.138"></a>
<FONT color="green">139</FONT>                                                   final UnivariateSolver lineSearchSolver) {<a name="line.139"></a>
<FONT color="green">140</FONT>            this(updateFormula,<a name="line.140"></a>
<FONT color="green">141</FONT>                 checker,<a name="line.141"></a>
<FONT color="green">142</FONT>                 lineSearchSolver,<a name="line.142"></a>
<FONT color="green">143</FONT>                 new IdentityPreconditioner());<a name="line.143"></a>
<FONT color="green">144</FONT>        }<a name="line.144"></a>
<FONT color="green">145</FONT>    <a name="line.145"></a>
<FONT color="green">146</FONT>        /**<a name="line.146"></a>
<FONT color="green">147</FONT>         * @param updateFormula formula to use for updating the &amp;beta; parameter,<a name="line.147"></a>
<FONT color="green">148</FONT>         * must be one of {@link Formula#FLETCHER_REEVES} or<a name="line.148"></a>
<FONT color="green">149</FONT>         * {@link Formula#POLAK_RIBIERE}.<a name="line.149"></a>
<FONT color="green">150</FONT>         * @param checker Convergence checker.<a name="line.150"></a>
<FONT color="green">151</FONT>         * @param lineSearchSolver Solver to use during line search.<a name="line.151"></a>
<FONT color="green">152</FONT>         * @param preconditioner Preconditioner.<a name="line.152"></a>
<FONT color="green">153</FONT>         */<a name="line.153"></a>
<FONT color="green">154</FONT>        public NonLinearConjugateGradientOptimizer(final Formula updateFormula,<a name="line.154"></a>
<FONT color="green">155</FONT>                                                   ConvergenceChecker&lt;PointValuePair&gt; checker,<a name="line.155"></a>
<FONT color="green">156</FONT>                                                   final UnivariateSolver lineSearchSolver,<a name="line.156"></a>
<FONT color="green">157</FONT>                                                   final Preconditioner preconditioner) {<a name="line.157"></a>
<FONT color="green">158</FONT>            super(checker);<a name="line.158"></a>
<FONT color="green">159</FONT>    <a name="line.159"></a>
<FONT color="green">160</FONT>            this.updateFormula = updateFormula;<a name="line.160"></a>
<FONT color="green">161</FONT>            solver = lineSearchSolver;<a name="line.161"></a>
<FONT color="green">162</FONT>            this.preconditioner = preconditioner;<a name="line.162"></a>
<FONT color="green">163</FONT>            initialStep = 1;<a name="line.163"></a>
<FONT color="green">164</FONT>        }<a name="line.164"></a>
<FONT color="green">165</FONT>    <a name="line.165"></a>
<FONT color="green">166</FONT>        /**<a name="line.166"></a>
<FONT color="green">167</FONT>         * {@inheritDoc}<a name="line.167"></a>
<FONT color="green">168</FONT>         *<a name="line.168"></a>
<FONT color="green">169</FONT>         * @param optData Optimization data.<a name="line.169"></a>
<FONT color="green">170</FONT>         * The following data will be looked for:<a name="line.170"></a>
<FONT color="green">171</FONT>         * &lt;ul&gt;<a name="line.171"></a>
<FONT color="green">172</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.MaxEval}&lt;/li&gt;<a name="line.172"></a>
<FONT color="green">173</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.InitialGuess}&lt;/li&gt;<a name="line.173"></a>
<FONT color="green">174</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.SimpleBounds}&lt;/li&gt;<a name="line.174"></a>
<FONT color="green">175</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.nonlinear.scalar.GoalType}&lt;/li&gt;<a name="line.175"></a>
<FONT color="green">176</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunction}&lt;/li&gt;<a name="line.176"></a>
<FONT color="green">177</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunctionGradient}&lt;/li&gt;<a name="line.177"></a>
<FONT color="green">178</FONT>         *  &lt;li&gt;{@link BracketingStep}&lt;/li&gt;<a name="line.178"></a>
<FONT color="green">179</FONT>         * &lt;/ul&gt;<a name="line.179"></a>
<FONT color="green">180</FONT>         * @return {@inheritDoc}<a name="line.180"></a>
<FONT color="green">181</FONT>         * @throws TooManyEvaluationsException if the maximal number of<a name="line.181"></a>
<FONT color="green">182</FONT>         * evaluations (of the objective function) is exceeded.<a name="line.182"></a>
<FONT color="green">183</FONT>         */<a name="line.183"></a>
<FONT color="green">184</FONT>        @Override<a name="line.184"></a>
<FONT color="green">185</FONT>        public PointValuePair optimize(OptimizationData... optData)<a name="line.185"></a>
<FONT color="green">186</FONT>            throws TooManyEvaluationsException {<a name="line.186"></a>
<FONT color="green">187</FONT>             // Retrieve settings.<a name="line.187"></a>
<FONT color="green">188</FONT>            parseOptimizationData(optData);<a name="line.188"></a>
<FONT color="green">189</FONT>            // Set up base class and perform computation.<a name="line.189"></a>
<FONT color="green">190</FONT>            return super.optimize(optData);<a name="line.190"></a>
<FONT color="green">191</FONT>        }<a name="line.191"></a>
<FONT color="green">192</FONT>    <a name="line.192"></a>
<FONT color="green">193</FONT>        /** {@inheritDoc} */<a name="line.193"></a>
<FONT color="green">194</FONT>        @Override<a name="line.194"></a>
<FONT color="green">195</FONT>        protected PointValuePair doOptimize() {<a name="line.195"></a>
<FONT color="green">196</FONT>            final ConvergenceChecker&lt;PointValuePair&gt; checker = getConvergenceChecker();<a name="line.196"></a>
<FONT color="green">197</FONT>            final double[] point = getStartPoint();<a name="line.197"></a>
<FONT color="green">198</FONT>            final GoalType goal = getGoalType();<a name="line.198"></a>
<FONT color="green">199</FONT>            final int n = point.length;<a name="line.199"></a>
<FONT color="green">200</FONT>            double[] r = computeObjectiveGradient(point);<a name="line.200"></a>
<FONT color="green">201</FONT>            if (goal == GoalType.MINIMIZE) {<a name="line.201"></a>
<FONT color="green">202</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.202"></a>
<FONT color="green">203</FONT>                    r[i] = -r[i];<a name="line.203"></a>
<FONT color="green">204</FONT>                }<a name="line.204"></a>
<FONT color="green">205</FONT>            }<a name="line.205"></a>
<FONT color="green">206</FONT>    <a name="line.206"></a>
<FONT color="green">207</FONT>            // Initial search direction.<a name="line.207"></a>
<FONT color="green">208</FONT>            double[] steepestDescent = preconditioner.precondition(point, r);<a name="line.208"></a>
<FONT color="green">209</FONT>            double[] searchDirection = steepestDescent.clone();<a name="line.209"></a>
<FONT color="green">210</FONT>    <a name="line.210"></a>
<FONT color="green">211</FONT>            double delta = 0;<a name="line.211"></a>
<FONT color="green">212</FONT>            for (int i = 0; i &lt; n; ++i) {<a name="line.212"></a>
<FONT color="green">213</FONT>                delta += r[i] * searchDirection[i];<a name="line.213"></a>
<FONT color="green">214</FONT>            }<a name="line.214"></a>
<FONT color="green">215</FONT>    <a name="line.215"></a>
<FONT color="green">216</FONT>            PointValuePair current = null;<a name="line.216"></a>
<FONT color="green">217</FONT>            int iter = 0;<a name="line.217"></a>
<FONT color="green">218</FONT>            int maxEval = getMaxEvaluations();<a name="line.218"></a>
<FONT color="green">219</FONT>            while (true) {<a name="line.219"></a>
<FONT color="green">220</FONT>                ++iter;<a name="line.220"></a>
<FONT color="green">221</FONT>    <a name="line.221"></a>
<FONT color="green">222</FONT>                final double objective = computeObjectiveValue(point);<a name="line.222"></a>
<FONT color="green">223</FONT>                PointValuePair previous = current;<a name="line.223"></a>
<FONT color="green">224</FONT>                current = new PointValuePair(point, objective);<a name="line.224"></a>
<FONT color="green">225</FONT>                if (previous != null) {<a name="line.225"></a>
<FONT color="green">226</FONT>                    if (checker.converged(iter, previous, current)) {<a name="line.226"></a>
<FONT color="green">227</FONT>                        // We have found an optimum.<a name="line.227"></a>
<FONT color="green">228</FONT>                        return current;<a name="line.228"></a>
<FONT color="green">229</FONT>                    }<a name="line.229"></a>
<FONT color="green">230</FONT>                }<a name="line.230"></a>
<FONT color="green">231</FONT>    <a name="line.231"></a>
<FONT color="green">232</FONT>                // Find the optimal step in the search direction.<a name="line.232"></a>
<FONT color="green">233</FONT>                final UnivariateFunction lsf = new LineSearchFunction(point, searchDirection);<a name="line.233"></a>
<FONT color="green">234</FONT>                final double uB = findUpperBound(lsf, 0, initialStep);<a name="line.234"></a>
<FONT color="green">235</FONT>                // XXX Last parameters is set to a value close to zero in order to<a name="line.235"></a>
<FONT color="green">236</FONT>                // work around the divergence problem in the "testCircleFitting"<a name="line.236"></a>
<FONT color="green">237</FONT>                // unit test (see MATH-439).<a name="line.237"></a>
<FONT color="green">238</FONT>                final double step = solver.solve(maxEval, lsf, 0, uB, 1e-15);<a name="line.238"></a>
<FONT color="green">239</FONT>                maxEval -= solver.getEvaluations(); // Subtract used up evaluations.<a name="line.239"></a>
<FONT color="green">240</FONT>    <a name="line.240"></a>
<FONT color="green">241</FONT>                // Validate new point.<a name="line.241"></a>
<FONT color="green">242</FONT>                for (int i = 0; i &lt; point.length; ++i) {<a name="line.242"></a>
<FONT color="green">243</FONT>                    point[i] += step * searchDirection[i];<a name="line.243"></a>
<FONT color="green">244</FONT>                }<a name="line.244"></a>
<FONT color="green">245</FONT>    <a name="line.245"></a>
<FONT color="green">246</FONT>                r = computeObjectiveGradient(point);<a name="line.246"></a>
<FONT color="green">247</FONT>                if (goal == GoalType.MINIMIZE) {<a name="line.247"></a>
<FONT color="green">248</FONT>                    for (int i = 0; i &lt; n; ++i) {<a name="line.248"></a>
<FONT color="green">249</FONT>                        r[i] = -r[i];<a name="line.249"></a>
<FONT color="green">250</FONT>                    }<a name="line.250"></a>
<FONT color="green">251</FONT>                }<a name="line.251"></a>
<FONT color="green">252</FONT>    <a name="line.252"></a>
<FONT color="green">253</FONT>                // Compute beta.<a name="line.253"></a>
<FONT color="green">254</FONT>                final double deltaOld = delta;<a name="line.254"></a>
<FONT color="green">255</FONT>                final double[] newSteepestDescent = preconditioner.precondition(point, r);<a name="line.255"></a>
<FONT color="green">256</FONT>                delta = 0;<a name="line.256"></a>
<FONT color="green">257</FONT>                for (int i = 0; i &lt; n; ++i) {<a name="line.257"></a>
<FONT color="green">258</FONT>                    delta += r[i] * newSteepestDescent[i];<a name="line.258"></a>
<FONT color="green">259</FONT>                }<a name="line.259"></a>
<FONT color="green">260</FONT>    <a name="line.260"></a>
<FONT color="green">261</FONT>                final double beta;<a name="line.261"></a>
<FONT color="green">262</FONT>                switch (updateFormula) {<a name="line.262"></a>
<FONT color="green">263</FONT>                case FLETCHER_REEVES:<a name="line.263"></a>
<FONT color="green">264</FONT>                    beta = delta / deltaOld;<a name="line.264"></a>
<FONT color="green">265</FONT>                    break;<a name="line.265"></a>
<FONT color="green">266</FONT>                case POLAK_RIBIERE:<a name="line.266"></a>
<FONT color="green">267</FONT>                    double deltaMid = 0;<a name="line.267"></a>
<FONT color="green">268</FONT>                    for (int i = 0; i &lt; r.length; ++i) {<a name="line.268"></a>
<FONT color="green">269</FONT>                        deltaMid += r[i] * steepestDescent[i];<a name="line.269"></a>
<FONT color="green">270</FONT>                    }<a name="line.270"></a>
<FONT color="green">271</FONT>                    beta = (delta - deltaMid) / deltaOld;<a name="line.271"></a>
<FONT color="green">272</FONT>                    break;<a name="line.272"></a>
<FONT color="green">273</FONT>                default:<a name="line.273"></a>
<FONT color="green">274</FONT>                    // Should never happen.<a name="line.274"></a>
<FONT color="green">275</FONT>                    throw new MathInternalError();<a name="line.275"></a>
<FONT color="green">276</FONT>                }<a name="line.276"></a>
<FONT color="green">277</FONT>                steepestDescent = newSteepestDescent;<a name="line.277"></a>
<FONT color="green">278</FONT>    <a name="line.278"></a>
<FONT color="green">279</FONT>                // Compute conjugate search direction.<a name="line.279"></a>
<FONT color="green">280</FONT>                if (iter % n == 0 ||<a name="line.280"></a>
<FONT color="green">281</FONT>                    beta &lt; 0) {<a name="line.281"></a>
<FONT color="green">282</FONT>                    // Break conjugation: reset search direction.<a name="line.282"></a>
<FONT color="green">283</FONT>                    searchDirection = steepestDescent.clone();<a name="line.283"></a>
<FONT color="green">284</FONT>                } else {<a name="line.284"></a>
<FONT color="green">285</FONT>                    // Compute new conjugate search direction.<a name="line.285"></a>
<FONT color="green">286</FONT>                    for (int i = 0; i &lt; n; ++i) {<a name="line.286"></a>
<FONT color="green">287</FONT>                        searchDirection[i] = steepestDescent[i] + beta * searchDirection[i];<a name="line.287"></a>
<FONT color="green">288</FONT>                    }<a name="line.288"></a>
<FONT color="green">289</FONT>                }<a name="line.289"></a>
<FONT color="green">290</FONT>            }<a name="line.290"></a>
<FONT color="green">291</FONT>        }<a name="line.291"></a>
<FONT color="green">292</FONT>    <a name="line.292"></a>
<FONT color="green">293</FONT>        /**<a name="line.293"></a>
<FONT color="green">294</FONT>         * Scans the list of (required and optional) optimization data that<a name="line.294"></a>
<FONT color="green">295</FONT>         * characterize the problem.<a name="line.295"></a>
<FONT color="green">296</FONT>         *<a name="line.296"></a>
<FONT color="green">297</FONT>         * @param optData Optimization data.<a name="line.297"></a>
<FONT color="green">298</FONT>         * The following data will be looked for:<a name="line.298"></a>
<FONT color="green">299</FONT>         * &lt;ul&gt;<a name="line.299"></a>
<FONT color="green">300</FONT>         *  &lt;li&gt;{@link InitialStep}&lt;/li&gt;<a name="line.300"></a>
<FONT color="green">301</FONT>         * &lt;/ul&gt;<a name="line.301"></a>
<FONT color="green">302</FONT>         */<a name="line.302"></a>
<FONT color="green">303</FONT>        private void parseOptimizationData(OptimizationData... optData) {<a name="line.303"></a>
<FONT color="green">304</FONT>            // The existing values (as set by the previous call) are reused if<a name="line.304"></a>
<FONT color="green">305</FONT>            // not provided in the argument list.<a name="line.305"></a>
<FONT color="green">306</FONT>            for (OptimizationData data : optData) {<a name="line.306"></a>
<FONT color="green">307</FONT>                if  (data instanceof BracketingStep) {<a name="line.307"></a>
<FONT color="green">308</FONT>                    initialStep = ((BracketingStep) data).getBracketingStep();<a name="line.308"></a>
<FONT color="green">309</FONT>                    // If more data must be parsed, this statement _must_ be<a name="line.309"></a>
<FONT color="green">310</FONT>                    // changed to "continue".<a name="line.310"></a>
<FONT color="green">311</FONT>                    break;<a name="line.311"></a>
<FONT color="green">312</FONT>                }<a name="line.312"></a>
<FONT color="green">313</FONT>            }<a name="line.313"></a>
<FONT color="green">314</FONT>        }<a name="line.314"></a>
<FONT color="green">315</FONT>    <a name="line.315"></a>
<FONT color="green">316</FONT>        /**<a name="line.316"></a>
<FONT color="green">317</FONT>         * Finds the upper bound b ensuring bracketing of a root between a and b.<a name="line.317"></a>
<FONT color="green">318</FONT>         *<a name="line.318"></a>
<FONT color="green">319</FONT>         * @param f function whose root must be bracketed.<a name="line.319"></a>
<FONT color="green">320</FONT>         * @param a lower bound of the interval.<a name="line.320"></a>
<FONT color="green">321</FONT>         * @param h initial step to try.<a name="line.321"></a>
<FONT color="green">322</FONT>         * @return b such that f(a) and f(b) have opposite signs.<a name="line.322"></a>
<FONT color="green">323</FONT>         * @throws MathIllegalStateException if no bracket can be found.<a name="line.323"></a>
<FONT color="green">324</FONT>         */<a name="line.324"></a>
<FONT color="green">325</FONT>        private double findUpperBound(final UnivariateFunction f,<a name="line.325"></a>
<FONT color="green">326</FONT>                                      final double a, final double h) {<a name="line.326"></a>
<FONT color="green">327</FONT>            final double yA = f.value(a);<a name="line.327"></a>
<FONT color="green">328</FONT>            double yB = yA;<a name="line.328"></a>
<FONT color="green">329</FONT>            for (double step = h; step &lt; Double.MAX_VALUE; step *= FastMath.max(2, yA / yB)) {<a name="line.329"></a>
<FONT color="green">330</FONT>                final double b = a + step;<a name="line.330"></a>
<FONT color="green">331</FONT>                yB = f.value(b);<a name="line.331"></a>
<FONT color="green">332</FONT>                if (yA * yB &lt;= 0) {<a name="line.332"></a>
<FONT color="green">333</FONT>                    return b;<a name="line.333"></a>
<FONT color="green">334</FONT>                }<a name="line.334"></a>
<FONT color="green">335</FONT>            }<a name="line.335"></a>
<FONT color="green">336</FONT>            throw new MathIllegalStateException(LocalizedFormats.UNABLE_TO_BRACKET_OPTIMUM_IN_LINE_SEARCH);<a name="line.336"></a>
<FONT color="green">337</FONT>        }<a name="line.337"></a>
<FONT color="green">338</FONT>    <a name="line.338"></a>
<FONT color="green">339</FONT>        /** Default identity preconditioner. */<a name="line.339"></a>
<FONT color="green">340</FONT>        public static class IdentityPreconditioner implements Preconditioner {<a name="line.340"></a>
<FONT color="green">341</FONT>            /** {@inheritDoc} */<a name="line.341"></a>
<FONT color="green">342</FONT>            public double[] precondition(double[] variables, double[] r) {<a name="line.342"></a>
<FONT color="green">343</FONT>                return r.clone();<a name="line.343"></a>
<FONT color="green">344</FONT>            }<a name="line.344"></a>
<FONT color="green">345</FONT>        }<a name="line.345"></a>
<FONT color="green">346</FONT>    <a name="line.346"></a>
<FONT color="green">347</FONT>        /**<a name="line.347"></a>
<FONT color="green">348</FONT>         * Internal class for line search.<a name="line.348"></a>
<FONT color="green">349</FONT>         * &lt;p&gt;<a name="line.349"></a>
<FONT color="green">350</FONT>         * The function represented by this class is the dot product of<a name="line.350"></a>
<FONT color="green">351</FONT>         * the objective function gradient and the search direction. Its<a name="line.351"></a>
<FONT color="green">352</FONT>         * value is zero when the gradient is orthogonal to the search<a name="line.352"></a>
<FONT color="green">353</FONT>         * direction, i.e. when the objective function value is a local<a name="line.353"></a>
<FONT color="green">354</FONT>         * extremum along the search direction.<a name="line.354"></a>
<FONT color="green">355</FONT>         * &lt;/p&gt;<a name="line.355"></a>
<FONT color="green">356</FONT>         */<a name="line.356"></a>
<FONT color="green">357</FONT>        private class LineSearchFunction implements UnivariateFunction {<a name="line.357"></a>
<FONT color="green">358</FONT>            /** Current point. */<a name="line.358"></a>
<FONT color="green">359</FONT>            private final double[] currentPoint;<a name="line.359"></a>
<FONT color="green">360</FONT>            /** Search direction. */<a name="line.360"></a>
<FONT color="green">361</FONT>            private final double[] searchDirection;<a name="line.361"></a>
<FONT color="green">362</FONT>    <a name="line.362"></a>
<FONT color="green">363</FONT>            /**<a name="line.363"></a>
<FONT color="green">364</FONT>             * @param point Current point.<a name="line.364"></a>
<FONT color="green">365</FONT>             * @param direction Search direction.<a name="line.365"></a>
<FONT color="green">366</FONT>             */<a name="line.366"></a>
<FONT color="green">367</FONT>            public LineSearchFunction(double[] point,<a name="line.367"></a>
<FONT color="green">368</FONT>                                      double[] direction) {<a name="line.368"></a>
<FONT color="green">369</FONT>                currentPoint = point.clone();<a name="line.369"></a>
<FONT color="green">370</FONT>                searchDirection = direction.clone();<a name="line.370"></a>
<FONT color="green">371</FONT>            }<a name="line.371"></a>
<FONT color="green">372</FONT>    <a name="line.372"></a>
<FONT color="green">373</FONT>            /** {@inheritDoc} */<a name="line.373"></a>
<FONT color="green">374</FONT>            public double value(double x) {<a name="line.374"></a>
<FONT color="green">375</FONT>                // current point in the search direction<a name="line.375"></a>
<FONT color="green">376</FONT>                final double[] shiftedPoint = currentPoint.clone();<a name="line.376"></a>
<FONT color="green">377</FONT>                for (int i = 0; i &lt; shiftedPoint.length; ++i) {<a name="line.377"></a>
<FONT color="green">378</FONT>                    shiftedPoint[i] += x * searchDirection[i];<a name="line.378"></a>
<FONT color="green">379</FONT>                }<a name="line.379"></a>
<FONT color="green">380</FONT>    <a name="line.380"></a>
<FONT color="green">381</FONT>                // gradient of the objective function<a name="line.381"></a>
<FONT color="green">382</FONT>                final double[] gradient = computeObjectiveGradient(shiftedPoint);<a name="line.382"></a>
<FONT color="green">383</FONT>    <a name="line.383"></a>
<FONT color="green">384</FONT>                // dot product with the search direction<a name="line.384"></a>
<FONT color="green">385</FONT>                double dotProduct = 0;<a name="line.385"></a>
<FONT color="green">386</FONT>                for (int i = 0; i &lt; gradient.length; ++i) {<a name="line.386"></a>
<FONT color="green">387</FONT>                    dotProduct += gradient[i] * searchDirection[i];<a name="line.387"></a>
<FONT color="green">388</FONT>                }<a name="line.388"></a>
<FONT color="green">389</FONT>    <a name="line.389"></a>
<FONT color="green">390</FONT>                return dotProduct;<a name="line.390"></a>
<FONT color="green">391</FONT>            }<a name="line.391"></a>
<FONT color="green">392</FONT>        }<a name="line.392"></a>
<FONT color="green">393</FONT>    }<a name="line.393"></a>




























































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